The scaled-particle theory and solvent isotope effects on the thermodynamic properties of inert solutes in water and methanol

The scaled-particle theory has been applied to the calculation of the thermodynamic changes associated with the formation of a cavity in several isotopic varieties of liquid water and methanol. From these results, the thermodynamic functions for the transfer of a cavity (or a hard-sphere solute) have been computed for the following solvent pairs: H₂OD₂O, H₂OH₂ ¹⁸O, H₂ ¹⁸OD₂ ¹⁸O, D₂OD₂ ¹⁸O, CH₃OHCH₃OD. For the last two of these solvents, density measurements required for the calculations were carried out as a function of temperature. The calculated deuterium solvent isotope effect on the heats and entropies of hard-sphere solutes in water is much greater than the¹⁸O isotope effect; the former also exhibits a more pronounced temperature dependence. The transfer functions computed for hard-sphere solutes are compared to experimental data on the transfer of various solutes from H₂O to D₂O and from CH₃OH to CH₃OD. In most of the cases examined, the cavity effect accounts for a large part of the transfer quantities measured for rare gases, hydrocarbons, and solutes containing a significant hydrocarbon substituent.